I try not to get too personal with online forums, but PLEASE DO NOT DO THIS!
I'm the product of abandonment by my own father and I despise him! It has created so many male issues for me and my brother is even worse! He has so many emotional problems that it has ruined his life, not too mention neither of us have had a positive intimate relationship EVER. I KNOW this is because I have a warped ideology of men from what my father did or actually did not do! I fear being left, as he did my mother and so I never fully give myself to a relationship! Don't do this to your children it will cut deeper then you could ever know if you leave them behind. They will NEVER forgive you for the pain this will cause them in life growing up and it will eat you alive everyday of your life! They will eventually come find you one day and you will be confronted with so much pain!
My father still refuses to contact me and I finally gave up after graduating college trying to have some sort of relationship with him. He gave excuse after excuse that were just lies to me! He was afraid my mother would put him back in jail (he was found in contempt for non-payment of support once) if he had contact with us, even at 20 y/o! Lies to make him feel better! I am now working with a counselor to try and repair my damaged view on men in hopes I do not pass it down to my own daughter.
Truly think about what your doing. STOP thinking of only yourself and do not use the excuse that they barely know who you are, because that is just a way for you to rationalize what you are doing to them and it's NOT rational!
I agree, with the previous poster. Unless you see yourself as a threat to these children in some way physically, you MUST remain in their lives! You DO NOT have to have a relationship with their mother, but it is your duty as the man that gave them life to honor that responsibilty.
Don't give up on them or yourself as a father! They have a right to you and to be loved by you! They did not ask for the life you gave them, so why should they be burdened by you leaving that life without good cause...good cause, meaning you could physically harm them if you had a relationship with them? That is the ONLY reason to terminate a parent/child relationship...ever!